{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Infinite Impulse Response-Filters (IIR)  <img src='data/images/logo.png' width=50 align='left'> \n",
    "\n",
    "author: Thomas Haslwanter \\\n",
    "date: June-2020\n",
    "\n",
    "In contrast to FIR-filters, IIR-filters can also include a *feedback* from the output to the input:\n",
    "\n",
    "<img src='data/images/IIR_filter.jpg' width=500>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import signal\n",
    "\n",
    "impulse = np.zeros(50)\n",
    "impulse[10] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: Impulse-Filtering\n",
    "\n",
    "As the name implies, an impulse input to an IIR-filter can have an arbitrarily long effect on the output. For example, take the filter:\n",
    "\n",
    "\\begin{equation}\n",
    "    y_i = x_i + \\frac{y_{i-1}}{2}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [1, -0.5]\n",
    "b = [1]\n",
    "impFiltered = signal.lfilter(b,a,impulse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Log ()')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 1, sharex=True)\n",
    "\n",
    "axs[0].plot(impulse)\n",
    "axs[0].plot(impFiltered,'*')\n",
    "axs[0].legend(['Input', 'Output'])\n",
    "axs[0].set_ylabel('Linear ()')\n",
    "\n",
    "axs[1].semilogy(impulse)\n",
    "axs[1].semilogy(impFiltered, '*')\n",
    "axs[1].set_xlabel('Points ()')\n",
    "axs[1].set_ylabel('Log ()')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you see in the *semilogy* output, the output gradually decreases - but goes on infinitely.\n",
    "\n",
    "## Example 2:  Lowpass\n",
    "\n",
    "A filter-type frequently used for bandpass-filtering are *Butterworth* filters.\n",
    "The *Butterworth-filter* is also called a *maximally flat* filter because it minimized transient artefacts in the filtered data.\n",
    "\n",
    "Butterworth filter can be *low-pass*, *high-pass*, or *band-pass*. Below a *bandpass* example.\n",
    "First, we demonstrate a low-pass filter:\n",
    "\n",
    "### Sample-data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Signal')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rate = 500\n",
    "t = np.arange(0,1,1/rate)\n",
    "freqs = [3, 50]\n",
    "amps = [2, 0.5]\n",
    "x = np.zeros(t.shape)\n",
    "for freq, amp in zip(freqs,amps):\n",
    "    x += amp * np.sin(2*np.pi*freq*t)\n",
    "    \n",
    "plt.plot(t,x)\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Signal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filter Characteristics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filter coefficients\n",
    "from scipy import signal\n",
    "Nyq = rate/2\n",
    "cutoff = 10\n",
    "b,a = signal.butter(4, cutoff/Nyq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the frequency response.\n",
    "w, h = signal.freqz(b, a, worN=8000)\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(0.5*rate*w/np.pi, np.abs(h), 'b')\n",
    "plt.semilogx(cutoff, 0.5*np.sqrt(2), 'ko')\n",
    "plt.axvline(cutoff, color='r')\n",
    "plt.xlim(1e-2, 0.5*rate)\n",
    "plt.title(\"Lowpass Filter Frequency Response\")\n",
    "plt.xlabel('Frequency [Hz]')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filtered Signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x25147f49cd0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Apply the filter to the noisy data\n",
    "filtered = signal.lfilter(b,a,x)\n",
    "\n",
    "plt.plot(t,x, label='rawdata')\n",
    "plt.plot(t,filtered, 'r', label='filtered')\n",
    "plt.xlabel('Time [sec]')\\\n",
    "\n",
    "plt.ylabel('Signal')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 3: \"filtfilt\" - Lowpass, without delay\n",
    "\n",
    "As you can see in the example above, *lfilter* induces a delay. For offline data analysis, this can be eliminated, by filtering the data twice: once forward, and once backward. This eliminates the delay, *but doubles the order of the filter*!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x251480318e0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ffiltered = signal.filtfilt(b,a,x)\n",
    "\n",
    "plt.plot(t,x, label='rawdata')\n",
    "plt.plot(t,ffiltered, 'g', label='filtfilt')\n",
    "plt.xlabel('Time [sec]')\\\n",
    "\n",
    "plt.ylabel('Signal')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 4: Bandpass\n",
    "\n",
    "For this, we first add a third frequency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our sample signal consists of three different frequencies. A bandpass, which contains only the middle frequency, should eliminate the upper an the lower frequency:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate = 10\n",
    "amps = np.r_[0.5, 1, 0.4]\n",
    "freqs = np.c_[[0.05, 0.3, 3]]\n",
    "omega = 2*np.pi * freqs\n",
    "\n",
    "t = np.arange(0, 40, 1/rate)\n",
    "x = amps @ np.sin(omega*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2514bd23dc0>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Butterworth filter\n",
    "nyq = rate/2       # [Hz]\n",
    "order = 5\n",
    "band = np.r_[0.2, 1]    # [Hz]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2514a79cb50>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(b_band, a_band) = signal.butter(5, band/nyq, btype='bandpass')\n",
    "filtered = signal.lfilter(b_band, a_band, x)\n",
    "plt.plot(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WARNING: Numerical Problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For higher frequencies, numerical problems can arise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Same as above, only with a higher sampling rate\n",
    "rate = 1000\n",
    "nyq = rate/2\n",
    "\n",
    "t = np.arange(0, 40, 1/rate)\n",
    "x = amps @ np.sin(omega*t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Still working\n",
    "If low-pass and high-pass are split into two different filters,\n",
    "the result is still correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2514ceb9c70>]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(b_low, a_low) = signal.butter(5, band[1]/nyq, btype='low')\n",
    "(b_high, a_high) = signal.butter(5, band[0]/nyq, btype='high')\n",
    "\n",
    "low_filtered = signal.lfilter(b_low, a_low, x)\n",
    "band_filtered = signal.lfilter(b_high, a_high, low_filtered)\n",
    "plt.plot(t, band_filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Failing\n",
    "The \"a/b format\" bandpass fails"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2514cf69430>]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(b_band, a_band) = signal.butter(5, band/nyq, btype='bandpass')\n",
    "filtered = signal.lfilter(b_band, a_band, x)\n",
    "plt.plot(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution: Second-order Sections Format\n",
    "\n",
    "Therefore it’s recommended to use *second-order sections format* when filtering, to avoid numerical error with transfer function (a/b) format for the bandpass:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2514bb8b1c0>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sos = signal.butter(5, band, 'bandpass', fs=rate, output='sos')\n",
    "filtered = signal.sosfilt(sos, x)\n",
    "plt.plot(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[5_FIR_Filters](5_FIR_Filters.ipynb)<img src=\"data\\images\\Forward_Backward.png\" align='middle'>[5_ImgProc_Intro](5_ImgProc_Intro.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
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